Difference between revisions of "Team:OUC-China/miniToe Family"

Revision as of 23:37, 14 October 2018

Team OUC-China: Main

miniToe Family

1. Background

1.1 The Four Keys in miniToe System

The wetlab members give us four important sites, Gln104, Tyr176, Phe155, His29, which play import roles in binding and cleavage in protein Csy4. Considering 20 kinds of amino acids, we have 80 mutants to explore and choose if we only have one site mutated.

Before we begin to design the protein mutants, we first looking into the working process of miniToe structure to find that which are the most important keys in our system.

Fig.1-1 The working process of miniToe system

All the reaction happened in our first system, miniToe, can be described chronologically by following five main steps.
(1)The miniToe structure is produced and accumulated.
(2)The Csy4 is produced with IPTG induced.
(3)The Csy4 binds to the miniToe structure and form the rm the Csy4-miniToe complex
(4)The Csy4 cleavage the special site and divide the miniToe structure into two parts: the Csy4-crRNA complex and the mRNA of sfGFP.
(5)The sfGFP is produced.
From the description above, we can get four key problems in our system to make sure that our system can work successfully:
(1)Does the Csy4 dock correctly with the miniToe structure (hairpin)?
(2)How about the binding ability between the Csy4 and miniToe structure (hairpin)?
(3)How about the cleavage ability between the Csy4 and miniToe structure (hairpin)?
(4)Does crRNA release from the RBS?
The most impressive way to explore four problems is to model our system at the atom level by molecular dynamics. And there are lots of work in exploring the Csy4-RNA complex by molecular dynamics.

1.2 Molecular Dynamics

Molecular dynamics (MD) is a computer simulation method for studying the physical movements of atoms and molecules. The atoms and molecules are allowing to interact for a fixed period of time, giving a view of the dynamic evolution of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, whose forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanics force fields.
To a system which consists of molecule or atoms, the total energy of a system includes kinetic energy and potential energy，which can be describe by the formula below: $E = {E_{kin}} + U$
where donates the kinetic energy and donates the potential energy.
In a molecule system, the total potential energy can be calculated by adding the 、 bond stretching potentials energy 、angle bending potentials energy 、torsion angle potentials energy 、out-of-plane potentials energy and some other cross effect together，which also can be describe by the formula below: $U = {U_{nb}} + {U_b} + {U_\theta } + {U_\phi } + {U_\chi } + {U_{cross}}$
This formula above also called the force field in molecular dynamics’ theory. There are many force field in the world that based on the statistical thermodynamics and empirical result. In the research of the protein and nucleic acid, the Amber force field is one of the best force field in the world. So we choose Amber as our force field and the formula of this field show below: \[\begin{array}{l} E = \sum\limits_{bond} {{K_b}{{({r_{ij}} - {r_0})}^2}} + \sum\limits_{angle} {{K_\theta }{{(\theta - {\theta _0})}^2}} + \sum\limits_{dihedral} {\frac{{{K_\phi }[1 + \cos (n\phi - {\phi _0})]}}{2}} \\ + \sum\limits_{impr} {\frac{{{K_\chi }[1 + \cos (n\chi - {\chi _0})]}}{2}} + \sum\limits_{nobond} {{\varepsilon _{ij}}\left[ {{{\left( {\frac{{R_{ij}^0}}{{{R_{ij}}}}} \right)}^{12}} - 2{{\left( {\frac{{R_{ij}^0}}{{{R_{ij}}}}} \right)}^6}} \right]} + \sum\limits_{nobond} {\frac{{{q_i}{q_j}}}{{{R_{ij}}}}} \end{array}\]
The items in the formula refers to bond stretching term、angle bending potentials、dihedral angle potentials、put of plane angle potentials、improper dihedral angle potentials、Van Der Waals interaction and Coulombic interaction terms in order.
Now considering the system which contains of consists of molecule or atoms in the classic mechanics, the atom or molecule can be characterized as follow:
The position of atom is , the speed of atom is , the acceleration of atom is , .
After the integral operation, we can get two formula of and : ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over v} _i} = {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over v} _i}^0 + {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over a} _i}t$
where the refers to initial speed and the refers to initial
According to the classic mechanics, the force applied to atoms is the negative gradient of potential energy: ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over F} _i} = - {\nabla _i}U = - \left( {\frac{\partial }{{\partial x}}\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over i} + \frac{\partial }{{\partial y}}\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over j} + \frac{\partial }{{\partial z}}\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over k} } \right)U$
Due to Newton’s second law, the acceleration of atom can also be described as: ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over a} _i} = \frac{{{{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over F} }_i}}}{{{m_i}}}$
Using the total formula above together, we can have the full process of the molecular dynamics described and the Fig.2-2 shows the flow chart of MD in program.

Fig.1-2 The flow chart of MD in program

1.3 Logic Line

When choosing the Csy4 mutants, we choose the four problems which discuss before as the four keys, and we choose the molecular dynamics as our main tools to look into our system in atom level. So what’s is the logic line between them?
We considering the mutants choosing-problem by following description:
What we know and proved by the experiment is that the wild-type Csy4 with miniToe system is working well, which means that all the important key problems we discussion did not exist in the wild-type Csy4. The wild-type Csy4 can dock correctly with the miniToe structure and the Csy4 have a good ability to bind and cleave the miniToe structure, finally the crRNA release from the RBS. So we choose the wild-type Csy4 as a standard, and all the Csy4 mutant can check the four key problems by comparing to wild-type Csy4.
So the four key problems transform into two main problem: how to describe four key problems and compare between the wild-type and mutant in mathematical ? That’s what we discuss in the following two part.

1.4 How to describe four key problems in mathematical form

We are going to check the molecular dynamics of wild-type in miniToe system to show you how to describe four key problems in mathematical form in this part.
For the first problem, we define a matrix called interaction matrix which can describe the interaction possibility between every amino acid of protein and every nucleic acid of hairpin, this interaction matrix can be calculate by the catRAPID graphic. We submit the wild-type Csy4 and miniToe structure respectively to online service and it can return us the interaction matrix. The Fig.1-3 is the heatmap of interaction matrix for wild-type Csy4 in hairpin region.

Fig.1-3 The heatmap of interaction matrix for wild-type Csy4.

And the rest three problems is solved by the molecular dynamics. The work of molecular dynamics is mostly based on the Jiří Šponer’s work, but still something different.
In order to explore the rest three key problems, we prepare two structure for the molecular dynamics. And the geometries of our miniToe system is based on the X-ray structure of Csy4/RNA complex with the cleaved RNA (PDB ID: 4AL5, resolution 2.0 A), it can be seen in the Fig.1-4.

Fig.1-4 the X-ray structure of Csy4/RNA complex

The first structure called precursor complex is preparing for the second and third problem: how about the binding ability and cleavage ability between the Csy4 and miniToe structure (hairpin)? The precursor complex consists of two part: wild-type Csy4 and miniToe structure that before cleaved. It describes the structure in the period the after the Csy4 binding to hairpin but didn’t cleave the hairpin in the special site. The Csy4 structure is coming from the X-ray structure we mention before while the minToe structure is constructed totally by the rational model: we put the sequence into the mFold to generate the secondary structure of hairpin then the tertiary structure is produced by the RNAComposer. The molecular docking between Csy4 and miniToe structure is carry out by PatchDock. The precursor complex of wild-type Csy4 can seem in the Fig.1-5

Fig.1-5. The precursor complex of wild-type Csy4

After getting the precursor complex, we begin to prepare for the simulation. Missing hydrogen atoms were add by PDBFixer, Force field we used is amber ff98SB. The system is immersed in a rectangular TIP3P water box. After minimizing energy of Protein/RNA system, we give some restriction to the RNA chain to make sure that the structure will not become an unreasonable structure when the temperature rise. All the reaction runs with the PBC condition under 300K and 1 atm in the NPT. The time step is 2 fs. The total simulation time is 50 ns. Gromacs and OpenMM are the most common software we used in Ubuntu 16.04 and Window10. The equipment we used is intel i7 6700HQ with the NVIDIA GTX 960M 4G, it can simulate about 100-150 ns per day under the GPU acceleration. And the trajectories result is analyze by Pymol and MDAnalysis. For the second problem, what we can get from the simulation data is protein binding free energy to describe the ability of binding. We use the data in 30-50 ns to calculate it, the 20 ns data in the beginning is aborted to make sure the structure is smooth when calculation. The result of binding free energy for wild-type Csy4 is . For the third problem, what we can get from the simulation data is some significant distance of key interaction in the active site of Csy4 to describe the ability of cleavage. Jiří Šponer points out some important key interactions of active site including Ser148(OG)-G20(O2’)、Ser150(OG)-G20(O3’)、Ser151(OG)-G20(N2’). By exploring Jiří Šponer’s work, we finally choose the Ser151(OG)-G20(N2’) as our mathematical form in tired problem. The distance curve of Ser151(OG)-G20(N2’) for wild-type Csy4 can be seem in Fig.1-6. We get the similar result comparing to Jiří Šponer’s work.

Fig.1-6. The distance of Ser151(OG)-G20(N2’) in wild-type Csy4

The second structure called product structure is preparing for the fourth problem: does crRNA release from the RBS. The product complex consists of two part: wild-type Csy4 and miniToe structure that after cleaved. It describes the structure in the period the after the Csy4 binding and cleaving the hairpin in the special site. The Csy4 structure is coming from the X-ray structure we mention before while the minToe structure which is cleaved constructed totally by the rational model: we put two RNA sequence into the SimRNAweb to finish the molecular docking of two chains RNA and generate the tertiary structure. And the molecular docking between Csy4 and miniToe structure is carry out by PatchDock. The product complex of wild-type Csy4 can seem in the Fig.1-7

Fig.1-7 The product complex of wild-type Csy4

We also explore the product complex by molecular dynamics follow the protocol mentioned before, but this time we only set the restriction to RBS chain while the crRNA chain is free in moving.
For the fourth problem, what we can get from the simulation data is the RMSD describing the structure movement for crRNA chain to be the mathematical form. We can see the RMSD in Fig.1-8. The RMSD is unstable which give an explain to experiment that crRNA is release from RBS.

Fig.1-8 The RMSD of the product complex of wild-type Csy4

1.5 How to compare four mathematical forms between wild-type and mutants

We are going to check the molecular dynamics of miniToe system with the mutant Csy4 to show you how to compare the four mathematical forms we choose before between the wild-type Csy4 and Csy4 mutants. In the following description, we give an example using the mutant Q104A to show you how to make comparing.

We first use the SwissModel to generate the tertiary structure with the template Csy4 (PDB ID: 4AL5, resolution 2.0 A). And using the molecular dynamics, we can get the four mathematical form showing in the Fig.1-9.

Fig.1-9 The four key problems in mathematical forms for Csy4-Q104A

Now we divided the four curves into two kind of data: the matrix and the numerical value. The interaction matrix and the curve can be regard as matrix because the curve is discrete, and the binding free energy is just an numerical value.
For the matrix we can use Euclidean distance to describe the difference between two matric: $D(p,{q_{WT}}) = \sqrt {\sum\limits_i^m {\sum\limits_j^n {{{({p_{i,j}} - {q^{WT}}_{i,j})}^2}} } } $ For the free bind ing energy, we used the formula below to calculate the difference between the wild type and mutant: $\ln ({K_{drel}}) = \ln (\frac{{{K_{dWT}}}}{{{K_{dMUT}}}}) = {G_{binding}}$
According to description above, we define four value used to compare four key problems between mutant and wild-type: ${D_1}({\mathop{\rm int}} teraction\mathop {}\limits^{} matrix)$ $\ln ({K_{drel}})$ ${D_3}(Ser151 - G20\mathop {}\limits^{} curve)$ ${D_4}(RMSD)$
For the mutant Q104A, the four is showing in the following chart

Csy4-Mutant	${D_1}$	$\ln ({K_{drel}})$	${D_3}$	${D_4}$
Q104A	0.483	2483	9.48	30.82

@@ Line 233: / Line 233: @@
 <br /><br />We first use the SwissModel to generate the tertiary structure with the template Csy4 (PDB ID: 4AL5, resolution 2.0 A). And using the molecular dynamics, we can get the four mathematical form showing in the Fig.1-9.						<div align="center"><img src="1.9" height="450">
 										</div>
-<div align="center"><p>Fig.1-9 The four key problems in mathematical forms for Csy4-Q104A</p></div>
+<div align="center"><p>Fig.1-9 The four key problems in mathematical forms for Csy4-Q104A</p></div> 					<br />	  Now we divided the four curves into two kind of data: the matrix and the numerical value. The interaction matrix and the curve can be regard as matrix because the curve is discrete, and the binding free energy is just an numerical value.
+<br />  For the matrix we can use Euclidean distance to describe the difference between two matric:
+		$D(p,{q_{WT}}) = \sqrt {\sum\limits_i^m {\sum\limits_j^n {{{({p_{i,j}} - {q^{WT}}_{i,j})}^2}} } } $				  For the free bind ing energy, we used the formula below to calculate the difference between the wild type and mutant:
+										$\ln ({K_{drel}}) = \ln (\frac{{{K_{dWT}}}}{{{K_{dMUT}}}}) = {G_{binding}}$
+	<br />   According to description above, we define four value used to compare four key problems between mutant and wild-type:
+							${D_1}({\mathop{\rm int}} teraction\mathop {}\limits^{} matrix)$
+			$\ln ({K_{drel}})$
+							${D_3}(Ser151 - G20\mathop {}\limits^{} curve)$
+										${D_4}(RMSD)$
+				<br /> 	  For the mutant Q104A, the four is showing in the following chart
+		<table width="200" border="1">
+  <tbody>
+    <tr>
+      <th scope="col">Csy4-Mutant</th>
+      <th scope="col">${D_1}$</th>
+      <th scope="col">$\ln ({K_{drel}})$</th>
+      <th scope="col">${D_3}$</th>
+      <th scope="col">${D_4}$</th>
+    </tr>
+    <tr>
+      <td>Q104A</td>
+      <td>0.483</td>
+      <td>2483</td>
+      <td>9.48</td>
+      <td>30.82</td>
+    </tr>
+  </tbody>
+</table>